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Considering the growing interest in magnetic materials for unconventional computing, data storage, and sensor applications, there is active research not only on material synthesis but also characterisation of their properties. In addition to structural and integral magnetic characterisations, imaging of magnetization patterns, current distributions and magnetic fields at nano- and microscale is of major importance to understand the material responses and qualify them for specific applications. In this roadmap, we aim to cover a broad portfolio of techniques to perform nano- and microscale magnetic imaging using SQUIDs, spin center and Hall effect magnetometries, scanning probe microscopies, x-ray- and electron-based methods as well as magnetooptics and nanoMRI. The roadmap is aimed as a single access point of information for experts in the field as well as the young generation of students outlining prospects of the development of magnetic imaging technologies for the upcoming decade with a focus on physics, materials science, and chemistry of planar, 3D and geometrically curved objects of different material classes including 2D materials, complex oxides, semi-metals, multiferroics, skyrmions, antiferromagnets, frustrated magnets, magnetic molecules/nanoparticles, ionic conductors, superconductors, spintronic and spinorbitronic materials.

Scanning SQUID susceptometry images the local magnetization and susceptibility of a sample. By accurately modeling the SQUID signal we can determine the physical properties such as the penetration depth and permeability of superconducting samples. We calculate the scanning SQUID susceptometry signal for a superconducting slab of arbitrary thickness with isotropic London penetration depth, on a non-superconducting substrate, where both slab and substrate can have a paramagnetic response that is linear in the applied field. We derive analytical approximations to our general expression in a number of limits. Using our results, we fit experimental susceptibility data as a function of the sample-sensor spacing for three samples: 1) delta-doped SrTiO3, which has a predominantly diamagnetic response, 2) a thin film of LaNiO3, which has a predominantly paramagnetic response, and 3) a two-dimensional electron layer (2-DEL) at a SrTiO3/AlAlO3 interface, which exhibits both types of response. These formulas will allow the determination of the concentrations of paramagnetic spins and superconducting carriers from fits to scanning SQUID susceptibility measurements., Comment: 11 pages, 13 figures

LaAlO3 and SrTiO3 are insulating, nonmagnetic oxides, yet the interface between them exhibits a two-dimensional electron system with high electron mobility,1 superconductivity at low temperatures,2-6 and electric-field-tuned metal-insulator and superconductorinsulator phase transitions.3,6-8 Bulk magnetization and magnetoresistance measurements also suggest some form of magnetism depending on preparation conditions5,9-11 and suggest a tendency towards nanoscale electronic phase separation.10 Here we use local imaging of the magnetization and magnetic susceptibility to directly observe a landscape of ferromagnetism, paramagnetism, and superconductivity. We find submicron patches of ferromagnetism in a uniform background of paramagnetism, with a nonuniform, weak diamagnetic superconducting susceptibility at low temperature. These results demonstrate the existence of nanoscale phase separation as suggested by theoretical predictions based on nearly degenerate interface sub-bands associated with the Ti orbitals.12,13 The magnitude and temperature dependence of the paramagnetic response suggests that the vast majority of the electrons at the interface are localized, and do not contribute to transport measurements.3,6,7 In addition to the implications for magnetism, the existence of a 2D superconductor at an interface with highly broken inversion symmetry and a ferromagnetic landscape in the background suggests the potential for exotic superconducting phenomena., Comment: Edited version to appear in Nature Physics

We use scanning SQUID microscopy to investigate the behavior of vortices in the presence of twin boundaries in the pnictide superconductor Ba(Fe1-xCox)2As2. We show that the vortices avoid pinning on twin boundaries. Individual vortices move in a preferential way when manipulated with the SQUID: they tend to not cross a twin boundary, but rather to move parallel to it. This behavior can be explained by the observation of enhanced superfluid density on twin boundaries in Ba(Fe1-xCox)2As2. The observed repulsion from twin boundaries may be a mechanism for enhanced critical currents observed in twinned samples in pnictides and other superconductors.

We calculate the change in susceptibility resulting from a thin sheet with reduced penetration depth embedded perpendicular to the surface of an isotropic superconductor, in a geometry applicable to scanning Superconducting QUantum Interference Device (SQUID) microscopy, by numerically solving Maxwell's and London's equations using the finite element method. The predicted stripes in susceptibility agree well in shape with the observations of Kalisky et al. of enhanced susceptibility above twin planes in the underdoped pnictide superconductor Ba(Fe1-xCox)2As2 (Ba-122). By comparing the predicted stripe amplitudes with experiment and using the London relation between penetration depth and superfluid density, we estimate the enhanced Cooper pair density on the twin planes, and the barrier force for a vortex to cross a twin plane. Fits to the observed temperature dependence of the stripe amplitude suggest that the twin planes have a higher critical temperature than the bulk, although stripes are not observed above the bulk critical temperature., Comment: 16 pages, 9 figures

We employed a scanning Hall probe microscope to detect the hopping of individual vortices between pinning sites along grain boundaries in YBCO thin films in the presence of an applied current. Detecting the motion of individual vortices allowed us to probe the current-voltage (I-V) characteristics of the grain boundary with voltage sensitivity below a femto-volt. We find a very sharp onset of dissipation with V~I^n with an unprecedented high exponent of n~290 that shows essentially no dependence on temperature or grain boundary angle. Our data have no straightforward explanation within the existing grain boundary transport models.

Measurements of the nonlinear flux-flow resistivity $\rho$ and the critical vortex velocity $\rm v^*_\phi$ at high voltage bias close to the instability regime predicted by Larkin and Ovchinnikov \cite{LO} are reported along the node and antinode directions of the d-wave order parameter in the \textit{a-b} plane of epitaxial $YBa_2Cu_3O_{7-\delta}$ films. In this pinning-free regime, $\rho$ and $\rm v^*_\phi$ are found to be anisotropic with values in the node direction larger on average by 10% than in the antinode direction. The anisotropy of $\rho$ is almost independent of temperature and field. We attribute the observed results to the anisotropic quasiparticle distribution on the Fermi surface of $YBa_2Cu_3O_{7-\delta}$., Comment: 5 figures

The dynamics of transient disordered vortex states in BSCCO was magneto-optically traced in three experiments: (i) during continuous injection of transient vortex states while ramping up the external magnetic field, (ii) during annealing of injected transient states while keeping the external field constant, and (iii) during annealing of transient 'supercooled' disordered states while ramping down the external field. The results reveal front-like propagation (experiment i) or retreat (experiments ii and iii) of the transient vortex states, at a rate governed by the rate of change of the external field, the annealing time tau of the transient states and the creep rate. The experimental results are theoretically analyzed in terms of competition between generation and annealing of transient disordered vortex states. Extraction of the annealing time tau from the above three experiments, yields the same results for tau as a function of the induction, B, and temperature T. Knowledge of tau(B,T) allows for correct determination of the thermodynamic order-disorder vortex phase transition line., Comment: Accepted to Phys. Rev. B